Unified picture of vibrational relaxation of OH stretch at the air/water interface

The elucidation of the energy dissipation process is crucial for understanding various phenomena occurring in nature. Yet, the vibrational relaxation and its timescale at the water interface, where the hydrogen-bonding network is truncated, are not well understood and are still under debate. In the present study, we focus on the OH stretch of interfacial water at the air/water interface and investigate its vibrational relaxation by femtosecond time-resolved, heterodyne-detected vibrational sum-frequency generation (TR-HD-VSFG) spectroscopy. The temporal change of the vibrationally excited hydrogen-bonded (HB) OH stretch band (ν=1→2 transition) is measured, enabling us to determine reliable vibrational relaxation (T1) time. The T1 times obtained with direct excitations of HB OH stretch are 0.2-0.4 ps, which are similar to the T1 time in bulk water and do not noticeably change with the excitation frequency. It suggests that vibrational relaxation of the interfacial HB OH proceeds predominantly with the intramolecular relaxation mechanism as in the case of bulk water. The delayed rise and following decay of the excited-state HB OH band are observed with excitation of free OH stretch, indicating conversion from excited free OH to excited HB OH (~0.9 ps) followed by relaxation to low-frequency vibrations (~0.3 ps). This study provides a complete set of the T1 time of the interfacial OH stretch and presents a unified picture of its vibrational relaxation at the air/water interface.

is approximately 3250 cm-1.The authors are well-aware of this.This frequency is far away from the free OH stretch frequency of 3700 cm-1.Even if as the authors suggest the reorientafion of water occurs such that the free OH get submerged into the bulk water, makes a hydrogen bond, lowering its frequency to enable for the efficient Fermi resonance -all these processes occur on long fime scales, definitely longer than 0.5 ps or so.The authors did not provide their esfimates for these fime scales.Therefore I cannot see how the free OH stretch relaxafion can be comparable or even faster.The authors should reconsider their kinefic models for potenfially missing contribufions.
-The authors rafionalize some of their result by referring to spectra diffusion, but no experimental results illustrafing OH stretch spectral diffusion at interface are given.I am wondering if two-dimensional SFG measurements can be done.If yes, and their results support the funding of this study than I would be more than happy to recommend this paper for publicafion in Nature Comm.In its present form the manuscript might be suitable for a more specialized journal.

Minor comments:
-Have the spectra in Fig. 1 been corrected for Fresnel factors?-Page 16: "In reality..." does this refer to experiments or modeling reality?
Reviewer #3 (Remarks to the Author): The authors have sought to determine the vibrafional relaxafion of the hydrogen bonded (HB) OH vibrafions of interfacial water, absent any contribufions from thermalizafion or ground state bleach.To do this, they measured the T1 fime for the 1->2 excited state of the HB-OH stretch while pumping on the 0->1 transifion of the HB-OH and free-OH stretch.Their work has shown the T1 fime is unaffected by the interfacial bonding environment and, thus, is the vibrafional relaxafion is the result of an intramolecular relaxafion mechanism.
Overall I found this work to be well executed, nicely communicated and of very high quality.It is suitable for publicafion in Nature Communicafions.There is, however, one point that it would be nice to hear the authors address.

Reply to Reviewer #1:
This manuscript describes TR-HD-SFG measurements of the OH stretch at the water-air interface in order to obtain the T1 relaxation time.This is in general an interesting topic that is fraught with controversies in the literature.
The new aspect of the present study is that the induced absorption from the 1 to 2 transition is investigated as opposed to previous efforts that have focused on the bleach of the 0 to 1 transition.This gives rise to a cleaner analysis than previous studies.
The experiments are carefully performed and the analysis solid.
We thank reviewer #1 for highly evaluating the experiments and analysis that we report in this paper.As the reviewer commented, we are very confident that the present study provided the most reliable T1 values of the OH stretch at the air/water interface.
However, I don't think that the advancement of our understanding of the relaxation dynamics of the air-water interface achieved in present study is not enough to warrant publication in Nature Communications, or any of the other Nature journals for that matter.

Reply:
Although the reviewer wrote that the advancement of our understanding provided by this paper is insufficient to warrant publication in Nature Communications, there are strong reasons that allow us to object to his/her comments.As we write in the introduction, molecular-level properties and dynamics of interfacial water are crucial for understanding many important chemical/physical processes in nature and industry, such as the formation of marine aerosol, on-water catalysis, protein folding, ice formation, functions of supramolecules in the aqueous phase, so on.The energy dissipation process is one of the most fundamental dynamics of interfacial water, and the T1 time of water OH stretch vibration is a prototypical measure of excess energy dissipation at interfaces.We stress that the T1 time of the OH stretch vibration even at the air/water interface is still very controversial although it is the simplest energy dissipation at the most fundamental water interface.Therefore, the unambiguous T1 time and the unified picture of the vibrational relaxation pathways provided by the present TR-HD-VSFG study provide a foundation for our solid understanding of the energy dissipation process at the liquid interfaces and the starting point for elucidating and controlling various interfacial phenomena.In fact, two other reviewers appreciate the significance of this work.
Furthermore, responding to the comments of other reviewers, we have revised the manuscript by adding new experimental data to Supplementary Information to show 1) ultrafast spectral diffusion of the hydrogen-bonded (HB) OH stretch is almost completed on the time scale of its T1 at the air/water interface, and 2) experimental evidence confirming that only excited-state HB OH signal appears in the low-frequency region investigated in the present study.With these additional experimental data, the quality and impact of the present paper became even greater than the original manuscript.
Therefore, we strongly believe that this paper meets the requirements for publication in Nature Communications because it provides decisive new knowledge about one of the most fundamental dynamics of interfacial water.

Reply to Reviewer #2:
In this manuscript Sung et al. used heterodyne detected sum-frequency generation spectroscopy (HD-SFG) to measure the rates of OH stretch vibrational relaxation in at water/air interface.This paper makes an important claim that the OH stretch vibrational lifetimes at the interface are comparable to those of bulk water which is in stark contrast to the previously published results.The authors claim that the improvement in experimental technique (HD-SFG vs homodyne SFG) and the "removal" of thermalized signal helped them measure the OH stretch relaxation better.While the authors has made a great effort in convincing the reader that they results are trustworthy, I am hesitant to recommend this paper for publication for the reasons described below.
We thank reviewer #2 for the careful reading and constructive comments.For the original manuscript, the reviewer was hesitant to recommend the publication for two major reasons: one related to the T1 time of the free OH stretch and the other related to the lack of experimental evidence of the ultrafast spectral diffusion which suppresses the frequency dependence of the T1 time.Carefully reading the reviewer's comments, we found that the first concern arose from a misunderstanding.To avoid such confusion, we made relevant changes in the revised manuscript.As for the second concern, we performed additional 2D experiments as suggested by the reviewer.The new data clearly indicated spectral diffusion is almost completed on the time scale of the T1 time.We believe these revisions with the additional data solve the reviewer's concerns.
We describe the details of our responses below.

Comment #1:
-As authors claim the mechanism for OH stretch relaxation at the interface is through Fermi resonance which is indeed an accepted view in the water community.The problem is that for Fermi resonance to be efficient the OH stretch frequency needs to be close to (2*HOH bend frequency -anharmonicity) which is approximately 3250 cm-1.The authors are well-aware of this.This frequency is far away from the free OH stretch frequency of 3700 cm-1.Even if as the authors suggest the reorientation of water occurs such that the free OH get submerged into the bulk water, makes a hydrogen bond, lowering its frequency to enable for the efficient Fermi resonance -all these processes occur on long time scales, definitely longer than 0.5 ps or so.The authors did not provide their estimates for these time scales.Therefore I cannot see how the free OH stretch relaxation can be comparable or even faster.The authors should reconsider their kinetic models for potentially missing contributions.

Reply:
Reading this comment of the reviewer, we realized that Figure 5 might have made him/her misunderstand the meaning of two T1 times (T1,HB and T1,free) obtained from the measurement with free OH excitation (3700 cm -1 ).
First, we would like to make it clear that we analyzed the relaxation of the excited free OH with the following relaxation scheme (i.e.formula (3) in the main text): Here, the signal observed in this study is that of excited HB OH (HB OH*).Based on this scheme, we described the relaxation process of the excited free OH stretch on page 23, line 1 as follows, "In the present HD-VSFG study, it was observed that the excited-state HB OH appears with excitation of the free OH with a time constant of 0.84 ± 0.08 ps.This time constant is essentially the same as the T1 time of the excited free OH (0.87 ± 0.06 ps) 44 that was determined from the recovery of GSB and the decay of the excited-state band of the free OH.Therefore, the observed excited-state HB OH is attributed to that converted from the excited free OH by the reorientation.In other words, the relaxation of the excited free OH proceeds with the reorientation motion of one OH moiety of a topmost water molecule while keeping its vibrational excitation." As clearly written above, the conversion time of an excited free OH stretch to an excited HB OH stretch is 1/k1, free (T1,free) = ~0.8-0.9 ps, and then the generated excited HB OH stretch, which has a much lower frequency, relaxes as an excited HB OH with 1/k1, HB (T1,HB) = ~0.3ps.Thus, the total time for the excited free OH stretch to dissipate its energy is ~1.1-1.2 ps.
To avoid any confusion, we note a peculiar feature of this relaxation scheme, that is, the generation time is the excited HB OH from the excited free OH (T1,free = ~0.8-0.9 ps) is longer than its decay time (T1,HB = ~0.3ps).In other words, once excited HB OH is formed from the excited free OH "slowly" by a reorientation, the generated excited HB OH relaxes very rapidly with a time constant of 0.3 ps.We stress that, nevertheless, the excited-state HB OH signal grows with the decay time of excited-state HB OH (T1,HB), while the excited-state HB OH signal decays with the formation time of excited-state HB OH (T1,free), as shown in Figure 4(b).This very counter-intuitive temporal behavior of the signal (and the population) simply arises from the relaxation scheme with T1,free > T1,HB, as we wrote in the 2 nd paragraph on page 17.
We are afraid that Figure 5 might have made the reviewer misunderstand this point and think that some portion of the excited free OH relaxes with T1,HB = ~0.3ps.To avoid such confusion, we revised Figures 5 and 6 in the revised main text to emphasize that the total relaxation time of the free OH stretch corresponds to the sum of the excited free OH → excited HB OH conversion time (T1,free = ~0.8-0.9 ps) and relaxation time of the generated excited HB OH (T1,HB = ~0.3ps).

Comment #2:
-The authors rationalize some of their result by referring to spectra diffusion, but no experimental results illustrating OH stretch spectral diffusion at interface are given.I am wondering if two-dimensional SFG measurements can be done.If yes, and their results support the funding of this study than I would be more than happy to recommend this paper for publication in Nature Comm.In its present form the manuscript might be suitable for a more specialized journal.

Reply:
We thank reviewer #2 for the suggestion of 2D HD-VSFG measurement.According to the reviewer's suggestion, we have measured the 2D HD-VSFG spectrum (2D Im (2) spectrum) of the air/water interface at 400 fs (Figure R1a).The observed bleach lobe of the HB OH stretch is vertically elongated along the pump frequency axis.In addition, the bandwidths of the bleach upon excitations at 3300, 3400, and 3500 cm -1 (Figure R1b) of the 1D slices are broad (~200 cm -1 FWHM) and look similar to each other although we can notice a slight difference in the spectral profile of the slice at highest pump frequency pump = 3500 cm -1 .This newly measured 2D HD-VSFG spectrum indicates that the spectral diffusion of the HB OH stretch at the air/water interface is almost completed on the time scale of the vibrational relaxation of the HB OH stretch which was determined in the present study.Therefore, ultrafast spectral diffusion is the most reasonable rationalization for the insensitivity of frequency dependence of the efficient vibrational relaxation of the HB OH stretch at the air/water interface.(b) 1D slices of the 2D HD-VSFG spectrumt at p =3500 cm -1 (top), 3400 cm -1 (middle), and 3300 cm -1 (bottom).
To describe the results of this new 2D HD-VSFG experiment, we revised the main text and added a new section in Supplementary Information.

Revision:
(Main text, Page 20, line 25) "To confirm ultrafast spectral diffusion at the air/water interface, we performed a 2D HD-VSFG measurement for the ground-state bleach region of the HB OH stretch.The 2D HD-VSFG spectrum obtained at 400 fs shows that the ground-state bleach lobe is almost completely elongated along the pump frequency axis, showing that the time scale of the spectral diffusion at the air/water interface is shorter than or, at least, comparable to the T1 time determined in the present study.(See Section S6 in Supplementary Information for the details.)The 2D HD-VSFG data support our argument that the T1 time of HB OH stretch is insensitive to the pump frequency because of the ultrafast spectral diffusion."(Supplementary Information, Page S19, line 1) S6. 2D HD-VSFG spectrum in the ground-state bleach region at 400 fs "To confirm the ultrafast spectral diffusion of the HB OH stretch at the air/water interface, we performed a 2D HD-VSFG measurement for the ground-state bleach region of the HB OH stretch (3200 -3550 cm -1 ) at 400 fs.The details of our 2D HD-VSFG setup and measurements have been reported elsewhere (Ref.40 in the main text).Briefly, we measured Im (2) spectra using five IR pump frequencies (pump) at 3200 cm -1 , 3300 cm - 1 , 3400 cm -1 , 3500 cm -1 , and 3600 cm -1 , and a 2D HD-VSFG spectrum (2D Im (2) spectrum) was constructed by combining five Im (2) spectra with interpolation along the pump axis (y-axis).It is noted that the bandwidth of the IR pump used in the present measurement is narrower (~120-150 cm -1 ) than that of the IR pump used in our first 2D HD-VSFG measurements at the air/water interface (~200 cm -1 ) (Ref.34 in the main text).(bottom), 3400 cm -1 (middle), and 3500 cm -1 (top).These three spectra show that the bandwidth of the positive bleaching band is similar (~200 cm -1 FWHM) although a subtle difference is noticed for the spectrum at pump=3500 cm -1 .Based on this 2D HD-VSFG spectrum at 400 fs, we can safely conclude that the time scale of the spectral diffusion at the air/water interface is shorter than or, at least, comparable to the T1 time of the HB OH stretch determined in the present study (the main text, Tables S2, and S3).This result strongly supports our argument that ultrafast spectral diffusion largely washes out the pump frequency dependence of the T1 time of the HB OH stretch at the air/water interface."

Reply:
The steady-state Im (2) spectrum of the air/water interface shown in the manuscript was not corrected by the Fresnel factor.We calculated the Fresnel factor and confirmed that the Fresnel factor correction does not change the Im (2) below 3100 cm -1 where the excited-state band of the HB OH stretch appears.
To make this point clear, we revised the main text and added a new section about the Fresnel factor correction in Supplementary Information, as follows.

Revision:
(Main text, Page 11, line 3) "Note that we did not perform the Fresnel factor correction for this analysis, because it does not affect the Im (2) spectra below 3100 cm -1 (see Section S7 in Supplementary Information)."(Supplementary Information, Page S21, line 1) S7.Fresnel factor correction on the Im (2) and Im (2) spectra of the air/water interface Fig. S9 compares Im (2) spectra at the air/water interface with and without the correction for the Fresnel factor.For the correction, we adopted the three-layer model (Shen, Y. R., Fundamentals of Sum-frequency Spectroscopy, Cambridge University Press (2016)) using two different refractive indices for the interface region: one is the refractive indices of bulk H2O (n'=nH2O) and the other is a value in between the refractive indices of air and bulk H2O (nair<n'<nH2O) which is estimated by applying the Lorentz model to the interface region (Zhuang et al.Phys.Rev. B 59, 12632 (1999).).Since nH2O in this frequency range significantly changes due to the vibrational resonance of water OH stretch, the modulation of the Fresnel factor of Lzz(2) becomes larger as the used n' value approaches nH2O.In fact, the largest effect of the Fresnel factor correction is seen when n' is set to nH2O (Fig. S9(a)).Nevertheless, the effect of the correction on the Im (2) spectrum is seen only above 3100 cm -1 where the IR absorption due to the OH stretch is significant, and the spectral region between 2900 and 3050 cm -1 , where the excited-state signal of the HB OH stretch appears, is not influenced even in this case.For a more realistic refractive index of the interface (nair<n'<nH2O), the Im (2) spectrum only exhibits a subtle shift of the HB OH stretch band after Fresnel factor correction, and the change below 3100 cm -1 is negligible (Fig S9 (b)).
Fig. S10 shows time-resolved Im (2) spectra measured with 3400-cm -1 excitation with and without the Fresnel factor correction. (For the convenience of comparison, we multiplied the magnitude of the Lyy(SF)Lyy(1)Lzz(2) making the amplitude of the Im (2) preserved.)We made the correction using the three-layer model with two interface refractive indices, as in the case of the steady-state Im (2) spectrum.Compared to the Im (2) spectra without the correction (Fig. S10 (a)), the Im (2) spectra after the correction using the two n' values only exhibit subtle changes in the frequency region above 3100 cm -1 (Fig. S10 (b) and (c)).Furthermore, the temporal profiles of the Im (2) signal integrated from 2900 cm -1 to 3050 cm -1 show almost no change with the Fresnel factor correction, and the evaluated T1,HB values are essentially the same (Fig. S11).These results of the analysis show that the effect of the Fresnel factor correction is negligible for the Im (2) spectra, temporal traces of the excited-state transition signal of the HB OH stretch, and evaluated T1 values discussed in the main text.

Reply:
In the original manuscript, it refers to both the experiment and model.To avoid unnecessary confusion, we remove this phrase on page 16 as follows,

Revision:
(page 16, line 16) "In the reality, however,.." (previous) "However,.." (present)     Reply to Reviewer #3: The authors have sought to determine the vibrational relaxation of the hydrogen bonded (HB) OH vibrations of interfacial water, absent any contributions from thermalization or ground state bleach.To do this, they measured the T1 time for the 1->2 excited state of the HB-OH stretch while pumping on the 0->1 transition of the HB-OH and free-OH stretch.Their work has shown the T1 time is unaffected by the interfacial bonding environment and, thus, is the vibrational relaxation is the result of an intramolecular relaxation mechanism.
Overall I found this work to be well executed, nicely communicated and of very high quality.It is suitable for publication in Nature Communications.There is, however, one point that it would be nice to hear the authors address.
We thank the reviewer for his/her very positive comments.For the question that the reviewer raised, we performed additional experiments to provide a clear answer, as described below.

Comment #1:
1.The authors highlight, several times, that the discrepancy between their work and previous work by the Bonn group (which measured the 0->1 HB-OH transition) is the result of a thermalization of the system.Is it possible for the authors to experimentally measure the dynamics of the thermalization process, to experimentally confirm its contribution?The authors determine a thermalization decay via the SVD, however it is noted that the error in the SVD determined values for the T_th is quite high (100% in some cases).Additionally, with respect to the SVD analysis, the error in some of the T_1 times are extraordinarily high (e.x.T_1,free for the 3700 cm-1 pump).Should the T_th times, in general, be considered with confidence?

Reply:
We thank the reviewer for careful reading and for letting us know the typo.We have corrected it.

REVIEWERS' COMMENTS
Reviewer #2 (Remarks to the Author): I am happy with the revised manuscript.I recommend publicafion but the following issue needs to be fixed first.Reviewer #3 (Remarks to the Author): The authors have sufficiently addressed my previous quesfion.The addifional experiments carried out to measure the dynamics of the thermalized and the spectral diffusion (in response to another reviewer's quesfion) are welcome addifions.
It is my opinion this arficle is of sufficient quality and significance for publicafion in Nature Communicafions, in its current form.The discussion, conclusions, and data sets included in this manuscript are immensely important to resolving inconsistencies in the literature surrounding the dynamics of interfacial water.
I congratulate the authors on a well-executed and thorough study.

Reply to Reviewer #2:
I am happy with the revised manuscript.I recommend publication but the following issue needs to be fixed first.

Reply:
According to the reviewer comment, we have corrected the typo in the caption of Figure S11 of Supplementary Information.We thank again reviewer #2 for careful reading.

Reply to Reviewer #3:
The authors have sufficiently addressed my previous question.The additional experiments carried out to measure the dynamics of the thermalized and the spectral diffusion (in response to another reviewer's question) are welcome additions.

It is my opinion this article is of sufficient quality and significance for publication in Nature
Communications, in its current form.The discussion, conclusions, and data sets included in this manuscript are immensely important to resolving inconsistencies in the literature surrounding the dynamics of interfacial water.I congratulate the authors on a well-executed and thorough study.

Reply:
We truly appreciate the reviewer #3's who recommended publication of our paper as it is.
Since he did not request any changes, we did not make any revisions on his/her comments.
Figure 5. T 1 time of the HB OH (red circle) and the free OH stretch (blue square) at the air/H 2 O

Figure 6 .
Figure 6.Schematic of the vibrational relaxation process of OH stretch at the air/H2O

Fig
Fig. S8(a) shows the 2D HD-VSFG spectrum obtained.The positive lobe in the 2D spectrum is nearly vertical along the pump axis, indicating that spectral diffusion is almost completed at 400 fs.Fig. S8(b) depicts the 1D horizontal slices of the 2D HD VSFG spectrum, which correspond to Im (2) spectra observed with the IR pump at 3300 cm -1

Figure S9 .
Figure S9.Im (2) spectrum at the air/water interface with and without the Fresnel factor correction.(a) Im (2) spectrum corrected with the interfacial refractive index set to the bulk H2O value (n'=nH2O).(b) Im (2) spectrum corrected with the interfacial refractive index estimated by applying the Lorentz model to the interface (nair <n'<nH2O).In both panels, Im (2) spectrum without the correction is also shown for the comparison.

Figure S10 .
Figure S10.Im (2) spectra at the air/water interface with and without the Fresnel factor correction.(a) Im (2) spectra without the Fresnel factor correction (same as Fig.2(c) in the main text).(b) Im (2) spectra corrected with the interfacial refractive index set to the bulk H2O value (n'=nH2O).(c) Im (2) spectra corrected with the interfacial refractive index estimated by applying the Lorentz model to the interface (nair <n'<nH2O).

Figure S11 .
Figure S11.Temporal traces of the Im (2) signal with and with the Fresnel factor correction.The Im (2) signal is obtained with the pump frequency at 3400 cm -1 .(a) Trace without Fresnel factor correction (same as Fig.3(c) in the main text).(b) Trace after the Fresnel factor correction with the interfacial refractive index set to the bulk H2O value (n'=nH2O).(c) Trace after the Fresnel factor correction corrected with the interfacial refractive index estimated by applying the Lorentz model to the interface (nair <n'<nH2O).

Figure S7 .
Figure S7.(a) Im (2) spectra in the IR probe range of 2900 -3550 cm -1 and the spectral decomposition based on SVD.Experimental data (shaded area), decomposed spectral components due to the excited-state transition + groud-state bleach bands of the HB OH stretch (red line), thermalized signal (blue line), and their sum (black line).The spectral profile of the broadband IR pump is shown on top of the Im (2) spectra.(b) Singular values obtained from the SVD analysis.(c) Spectral components due to excited-state and ground-state bleach bands (top) and thermalized signal (bottom).(d) Temporal traces of the two decomposed spectral components.

Figure S11 .
Figure S11.Caption."signal with and with the Fresnel..." should be "with and without".